Four-fermion Coupling Research Articles

Auxiliary field method in 4- and 3-dimensional Nambu–Jona-Lasinio models

In order to check the validity of the auxiliary field method in the Nambu--Jona-Lasinio model, the one-loop (= quantum) effects of auxiliary fields on the gap equation are considered with N-component fermion models in four and three dimensions. N is not assumed very large but is regarded as a loop expansion parameter. To overcome infrared divergences caused by the Nambu-Goldstone bosons, an intrinsic fermion mass is assumed. It is shown that the loop expansion can be justified by this intrinsic mass whose lower limit is also given. It is found that due to quantum effects, chiral symmetry breaking (\ensuremath{\chi}SB) is restored in $D=4$ and $D=3$ when the four-Fermi coupling is large. However, \ensuremath{\chi}SB is enhanced in a small coupling region in $D=3.$

Phase diagram of compact QED coupled to a four-Fermi interaction

Compact lattice quantum electrodynamics with four species of fermions is simulated with massless quarks by adding a four-Fermi interaction to the action. Simulations in the chiral limit are done on ${8}^{4}$ lattices for exploratory purposes, and ${16}^{4}$ lattices for quantitative purposes, and the phase diagram, parametrized by the gauge and the four-Fermi couplings, is mapped out. The line of monopole condensation transitions is separate from the line of chiral symmetry restoration as long as the four-Fermi coupling is not too small. The simulation results indicate that the monopole condensation transition is first order while the chiral transition is second order. The challenges in determining the universality class of the chiral transition are discussed. If the scaling region for the chiral transition is sufficiently wide, the ${16}^{4}$ simulations predict critical indices far from mean field values. We briefly discuss a speculative scenario in which antiscreening provided by strands of bound monopole and antimonopole loops is the agent that balances the screening of fermion-antifermion pairs to produce ultraviolet stable fixed points.

Bhabha versus Møller scattering as a contact-interaction analyzer at a polarized Linear Collider

We discuss electron-electron contact-interaction searches in the Bhabha and Moller processes at planned Linear Colliders run in the electron-positron and electron-electron modes, with longitudinally polarized beams. Our analysis is based on the measurement, for the two processes, of polarized differential cross sections that allow to disentangle the different, independent, four-fermion couplings. We evaluate by a model-independent analysis the sensitivities to the contact coupling constants, emphasizing the role of the available beam polarization and the complementarity of the two processes in giving the best limits. We also make a comparison with the potential of $e^+e^-\to\mu^+\mu^-$ at the same energy and beams polarization.

D-brane models with non-linear supersymmetry

We study a class of type I string models with supersymmetry broken on the world-volume of some D-branes and vanishing tree-level potential. Despite the non-supersymmetric spectrum, supersymmetry is non-linearly realized on these D-branes, while it is spontaneously broken in the bulk by Scherk–Schwarz boundary conditions. These models can easily accommodate 3-branes with interesting gauge groups and chiral fermions. We also study the effective field theory and in particular we compute the four-fermion couplings of the localized goldstino with the matter fermions on the brane.

Effect of dynamicalSU(2)gluons to the gap equation of the Nambu–Jona-Lasinio model in a constant background non-Abelian magnetic field

In order to estimate the effect of dynamical gluons to chiral condensate, the gap equation of SU(2) gauged Nambu--Jona-Lasinio model, under a constant background magnetic field, is investigated up to the two-loop order in 2+1 and 3+1 dimensions. We set up a general formulation allowing both cases of electric as well as magnetic background field. We rely on the proper time method to maintain gauge invariance. In 3+1 dimensions chiral symmetry breaking ($\chi$SB) is enhanced by gluons even in zero background magnetic field and becomes much striking as the background field grows larger. In 2+1 dimensions gluons also enhance $\chi$SB but whose dependence on the background field is not simple: dynamical mass is not a monotone function of background field for a fixed four-fermi coupling.

Gluonic contributions in a four-fermion interaction model

The gap equation for the fermion in nuclear medium is obtained in a two-flavor gauged Nambu--Jona-Lasino (NJL) model using the Schwinger-Dyson (SD) equations. The gap equation is solved with a quenched truncation. Compared to the four-fermion interaction, the one-gluon-exchange interaction accounts for considerable contributions (about $15\ensuremath{-}50%)$ to dynamically generated fermion mass. With incorporation of gluonic contributions into a scheme where there is only four-fermion interaction, the four-fermion coupling constant is made density dependent. Impacts of the density-dependent four-fermion (DDFF) coupling constants on quantities, such as the fermion mass and the chiral order parameter as well as masses of mesons (\ensuremath{\sigma},\ensuremath{\pi}), are estimated. The DDFF coupling constants lead to less density dependence of hadron masses and the larger critical density of chiral symmetry restoration than those from the pure four-fermion interaction. The calculated quantities are somehow dependent on the confinement scale ${\ensuremath{\Lambda}}_{\mathrm{QCD}}.$ However, the range of ${\ensuremath{\Lambda}}_{\mathrm{QCD}}$ in the present parametrization can be determined by the saturation property of the gluonic contribution in the medium and it turns out quite small.

Spinons and holons on the lattice

We point out that the dynamical fermion mass generation in the 3D compact U(1) lattice gauge theory with charged fermion and scalar fields (χ Uφ 3 model) may be of relevance for the spinon-holon theory with local gauge symmetry in the condensed matter physics. However, many properties of the χ Uφ 3 model are uncertain, so we make some conjectures to motivate their future investigation. Most probably, for strong gauge coupling the model is by universality equivalent to the familiar 3D four-fermion coupling models with N f = 2. Available numerical results indicate that at the intermediate and weak gauge coupling two universality classes with new interesting physics may arise. One of them is associated with a tricritical point which probably exists in the phase diagram of the χ Uφ 3 model. The other one is determined by the dynamical fermion mass generation in the compact QED 3, which is insufficiently understood but of much interest by itself.

Nonperturbative infrared dynamics of three-dimensional QED with a four-fermion interaction

A non-linear Schwinger-Dyson (SD) equation for the gauge boson propagator of massless QED in one time and two spatial dimensions is studied. It is shown that the nonperturbative solution leads to a nontrivial renormalization-group infrared fixed point quantitatively close to the one found in the leading order of the 1/N expansion, with N the number of fermion flavors. In the gauged Nambu-Jona-Lasinio (GNJL) model an equation for the Yukawa vertex is solved in an approximation given by the one-photon exchange and an analytic expression is derived for the propagator of the scalar fermion-antifermion composites. Subsequently, the mass and width of the scalar composites near the phase transition line are calculated as functions of the four-fermion coupling g and flavor number N. The possible relevance of these results for describing particle-hole excitations, in particular antiferromagnetic correlations, observed in the underdoped cuprates, is briefly discussed.

Two-higgs doublet model from quasilocal quark interactions

Quark models with four-fermion interaction including derivatives of fields in the strong coupling regime are used to implement composite-Higgs extensions of the standard model. In this approach, the dynamical breaking of chiral symmetry occurs in two (or more) channels (near polycritical values for coupling constants), which gives rise to two (or more) composite Higgs doublets. Two types of models are built for which the flavor-changing neutral currents (FCNC) are naturally suppressed. In model I, the second Higgs doublet is regarded as a radial excitation of the first one. In model II, at low energies, the quasilocal Yukawa interaction with Higgs doublets reduces to a conventional local one where each Higgs doublet couples to a definite charge current and its vacuum expectation value brings the mass either to up- or to down-components of fermion doublets. For a special configuration of four-fermion coupling constants, the dynamical CP-violation in the Higgs sector appears as a result of complexity of the the vacuum expectation value (v.e.v.) for Higgs doublets. Bibliography: 32 titles.

Model independent constraints on contact interactions from LEP2

We quantitatively discuss the possibility of deriving model-independent constraints on the general four-fermion contact interaction couplings, from the currently available data on the two-fermion production processes e + e −→ μ + μ −, b b ̄ and c c ̄ with unpolarized initial beams. The method is essentially based on particular, simple, combinations of the measured total cross section and forward–backward asymmetry that allow partial separation of the helicity cross sections, and the combination of experimental data obtained at the different energies of TRISTAN, LEP1 and LEP2.

Aspects of high density effective theory in QCD

We study an effective theory of QCD at high density in detail, including the finite temperature effects and the leading order correction in $1/\mu$ expansion. We investigate the Cooper pair gap equation and find that the color-flavor locking phase is energetically preferred at high density. We also find the color-superconducting phase transition occurs in dense quark matter when the chemical potential is larger than $250\pm 100~{\rm MeV}$ and the temperature is lower than 0.57 times the Cooper pair gap in the leading order in the hard-dense-loop approximation. The quark-neutrino four-Fermi coupling and the quark-axion coupling receive significant corrections in dense quark matter.

The four-fermi coupling of the supersymmetric non-linear σ -model on G/S⊗{U(1)}

The reducible K\"ahler coset space G/S\otimesU(1)^k is discussed in a geometrical approach. We derive the formula which expresses the Riemann curvature of the reducible K\"ahler coset space in terms of its Killing vectors. The formula manifests the group structure of G. On the basis of this formula we establish an algebraic method to evaluate the four-fermi coupling of the supersymmetric non-linear sigma-model on G/S\otimesU(1)^k at the low-energy limit. As an application we consider the supersymmetric non-linear sigma-model on E_7/SU(5)\otimesU(1)^3 which contains the three families of {10} + {5^*} + {1} of SU(5) as the pseudo NG fermions. The four-fermi coupling constants among diffferent families of the fermions are explicitly given at the low-energy limit.

FINE-TUNING THE LOW-ENERGY PHYSICS

In this letter we discuss the problem of the extreme fine-tuning necessary to achieve the quark mass scale mt within the dynamical symmetry breaking of the phenomenological [Formula: see text] condensate model. Inspired by the vector-like phenomenon of chiral gauge theories at short distances, we postulate that the W±-gauge bosons possess a vector-like gauge coupling and contribute to the gap-equations of quark self-energy functions in the high-energy region. We find that the gap-equations of different charge sectors are coupled, and as a result the unnatural fine-tuning is overcome and the ratio of the top and bottom masses is related to the electric charge: [Formula: see text], provided the quadratic divergence is removed by setting the four-fermion coupling [Formula: see text].

Functional Integral in Terms of the Field Strength: An Approach to Chiral Symmetry Breaking

The chiral symmetry breaking in the 4-dimensional QED with the chirally invariant four-fermion interaction is discussed by using a novel path integral expression in terms of the field-strength tensor. In the local potential approximation, we find that the chiral symmetry is spontaneously broken for any nonzero gauge and four-fermion couplings on the tree level of an auxiliary field $\sigma$. The present approach allows us to easily include higher orders of the gauge coupling so that the effective potential up to the sixth order is obtained.

CLEO results on tau Michel parameters

We present measurements of the tau Michel Parameters made by the CLEO experiment. Three different analyses are performed: a spin-independent lepton spectrum analysis and a second spin-dependent analysis using ℓ ± vs. π ‡π 0 events, and a third spin-dependent analysis using π + vs. π − events. the results are used to derive limits on the general four-fermion couplings, the mass of the charged Higgs in the MSSM, and a right-handed W in left-right models. Many of these measurements are more precise than the PDG world averages.

COMPOSITE TWO-HIGGS MODELS (GENERAL PART)

Quark models with four-fermion interaction including derivatives of fields in the strong coupling regime are used to implement composite-Higgs extensions of the Standard Model. In this approach the dynamical breaking of chiral symmetry occurs in two (or more) channels (near polycritical values for coupling constants), giving rise to two (or more) composite Higgs doublets. Two types of models are built for which Flavor Changing Neutral Currents (FCNC) are naturally suppressed. In the first Model I the second Higgs doublet is regarded as a radial excitation of the first one. In the second Model II the quasilocal Yukawa interaction with Higgs doublets reduces at low energies to a conventional local one where each Higgs doublet couples to a definite charge current and its v.e.v. brings the mass either to up- or to down-components of fermion doublets. For the special configuration of four-fermion coupling constants the dynamical CP violation in the Higgs sector appears as a result of complexity of v.e.v. for Higgs doublets.

On the low-energy effective action of N = 2 supersymmetric Yang-Mills theory

We investigate the perturbative part of Seiberg's low-energy effective action of N = 2 supersymmetric Yang-Mills theory in Wess-Zumino gauge in the conventional effective field theory technique. Using the method of constant field approximation and restricting the effective action with at most two derivatives and not more than four-fermion couplings, we show some features of the low-energy effective action given by Seiberg based on U(1) R anomaly and non-perturbative β-function arguments.

Fermion Self-Energy and Chiral Symmetry Breaking from Four-Fermion and Gauge Interactions**The project supported partially by National Natural Science Foundation of China and by Grant No. LWTZ-1298 of the Chinese Academy of Sciences

The exact analytic solutions of the linearized Schwinger–Dyson equation of fermion self-energy are used to obtain the effective four-fermion and gauge coupling criticality curves for dynamical chiral symmetry breaking. The results show that when the zero-momentum gauge coupling , the critical gauge coupling in the pure gauge interaction case, the minimal critical four-fermion coupling is always nonzero and positive and will go up as the decreases. The use of the exact solutions also allows us to make quite definite estimations of the momentum scales where chiral symmetry breaking would happen if the values of an infrared parameter are given separately.

Finite density QCD with chiral-invariant four-fermion interactions

A mean field analysis of finite density QCD is presented including the effects of additional chiral-invariant four-fermion interactions. A lattice regularization is used with ${N}_{f}=4$ flavors of staggered fermions. The use of the four-fermion coupling as an improved extrapolation parameter over the bare quark mass in Monte Carlo simulations is discussed. Particular attention is given to the structure of the phase diagram and the order of the chiral phase transition. At zero gauge coupling, the model reduces to a Nambu--Jona-Lasinio model. In this limit the chiral phase transition is found to be second-order near the zero-density critical point and otherwise first order. In the strong gauge coupling limit a first-order chiral phase transition is found. In this limit the additional four-fermion interactions do not qualitatively change the physics. The results agree with previous studies of QCD as the four-fermion coupling vanishes.

Chiral Symmetry Breaking in Strongly Coupled U(1) Gauge Theory Coupled to Scalar and Fermion Matter

We construct a transformation for scalar QED (U(1) gauge theory coupled with a charged scalar field) which leads to a dual effective gauge theory having a perturbation theory expansion in inverse powers of the (electric charge) coupling constant. The dual formulation is applied to the special case of scalar QED coupled to a massless charged fermion. A four-fermion interaction term arises naturally under the duality mapping. As an extension to discussions initiated by Miransky, Bardeen and Kondo and their collaborators in the late 1980's, we use this formulation to explore the possibility of a dynamical breakdown of chiral symmetry for the strongly coupled U(1) gauge theory interacting with both scalar and fermion degrees of freedom. Assuming that scalar QED is realized in the Higgs phase, we examine the Schwinger–Dyson equation approach to the fermion propagator in next-to-leading order of the strong coupling expansion (quenched approximation, i.e. no fermion loops). We construct a consistent renormalization procedure to deal with the ultraviolet infinities. For fixed scalar field vacuum expectation values, we obtain in the plane of the two important parameters of the theory (electric charge and four-fermion coupling constant) critical transition lines to a chirality broken phase.